HL AI - Analyzing Data (stats)

Population

an entire group of individuals that information is being collected about

Census

collects data from every individual in the population

Sample

collects data from a subset of individuals in the population

Bias

when a study consistently under- or over-estimates data due to how it was collected

Convenience Sampling

choosing individuals who are easiest to reach (choose conveniently, no strata)

Quota Sampling

a sampling technique where a population is divided into groups and then participants are chosen conveniently (choose conveniently, with strata)

Simple Random Sampling

every member of the population has an equal probability of being selected for the sample (choose randomly, no strata)

Stratified Sampling

a population is divided into a strata then chosen randomly (choose randomly, with a strata)

Systematic Sampling

created by selecting members of the population at regular intervals, eg. every tenth person on a lit of people in UWC grade 11 (choose randomly, no strata)

Bivariate Data

data showing the relationship between two variables

Continuous Data

data that can take any value within a range, with no discrete groups (eg. height, arm span, etc)

Discrete Data

when only a certain number of values are possible and there are no intermediates between groups (eg. eye color, number of siblings, etc)

Cumulative Frequency

the total frequency up to a certain data value

Correlation

the degree of association between two variables (can be positive or negative)

Outlier

a value that is far outside the general range of data (Q1 - 1.5 x the IQR) or (Q3 + 1.5 x the IQR)

Standard Deviation

the measure of how much a set of values differs from its mean (a measure of spread)

When you add to each data point…

• average (mean, median, mode) increases by the number added

• spread (IQR, range, standard deviation, variance) stays the same

When you multiply each data point…

• average (mean, median, mode) is multiplied by the same number

• spread (IQR, range, standard deviation, variance) is also multiplied by the same number

Variance

the square of a data set’s standard deviation (so outliers are weighed more heavily than data that is closer to the mean)

Pearson’s Correlation Coefficient

a measure of the linear relationship between two variables, and it is used on the raw data (affected more by outliers)

Spearman’s Correlation Coefficient

a measure of the monotonic relationship between the rank of two variables, and it is used on ranked data (affected less by outliers)

Reliability of data can be compromised by…

• missing data

• small sample size

• errors in handling

• outliers

Causation Disclaimer

must remember that correlation between variables does not necessarily mean one causes the other

Extrapolation

estimating or predicting values beyond the known data points (could lead to incorrect predictions)

s vs σ

• s represents the spread in the entire population if you are looking at a sample

• σ represents the spread in the entire population only if you are looking at the entire population

Reliability

when a test produces similar results each time it is carried out

Validity

when a test measures what it claims to measure

Test-Retest

a technique to increase reliability by repeating the same test with the same people at different times

Parallel Forms

a technique to increase reliability by doing different tests with the same people at the same time

Content Validity

refers to whether a test is actually answering the question it is trying to test for

Criterion Validity

the extent to which one test can predict the outcome of another test (eg. mock exams and ib exams)